Grain Loading-2 (Voids and Volumetric Heeling Moments)

Q. Why on a ship loaded with grain due account of voids must be taken? How is it done?
During the movement of ship grain settles downwards by 2%. The grain during a shift moves upwards with respect to the ship. The ship however, lists towards the shifted side. Considering this in the grain code, the grain is set to shift to low side, which actually means listed side. This also means the voids shift on the other side (high side). A void increases due to settling of grain.  Voids exist above all free grain surfaces in filled compartments. The extent of the voids depends on the dimensions of the compartment and the depth from the overhead to the grain surface. Assumption is made in respect of void depth and the angle to which the grain surface will be with respect to horizontal.

Grain heeling moments are produced by a grain shift. Grain heeling moment is the product of the volume of the shifted grain multiplied by the horizontal distance between its initial and final centres of gravity. Volumetric heeling moments are expressed in m4. It is also assumed to be equal to the volume of void multiplied by shift of their centroid.

Q. In the grain stability book, why the volumetric heeling moments are used and not the weight heeling moment?
Volumetric heeling moment is the product of the volume of grain that would shift multiplied by athwartship distance through which it would shift. It is common practice to calculate and tabulate the volumetric heeling moment of different compartments instead of weight heeling moment. A ship may load the grain of different stowage factors. To obtain the actual weight heeling moment for a particular grain the volumetric heeling moment is divided by the stowage factor of that grain.

Q. How is the data about volumetric heeling moment provided on ships?
Volumetric heeling moments are calculated by naval architects and tabulated in the vessel’s approved grain booklet. The grain stability booklet is required for vessel engaged in the carriage of bulk grain. Calculations can be complex-depending on the geometry of the compartment. In approved grain stability booklet the volumetric heeling moments are represented for individual compartments in either curved form or in tabulated form enabling the user to find the volumetric heeling moments for the full and slack conditions.

A sample table of maximum volumetric heeling moment for partly filled compartment

Q. What information is provided in the triple curve in respect of the different holds of a grain carrier ship?
The curves for each hold are provided to give KG, volume and volumetric heeling moment for the cargo loaded and can be entered with the argument viz. depth from the tank top or ullage from the hatch coaming.
It can be seen that the volumetric heeling moment is zero at the base, maximum for half filled hold and minimal for the filled condition. KG for the present loaded condition can be obtained from the graph but KG for the complete compartment (geometric centroid) can be obtained from the tables.

Q. What allowance is made for the vertical shift of grain?
When grain shifts on a ship there is a net vertical upwards movement of the center of gravity of the grain which in turn raises the center of gravity of the ship and reduces the GM. In calculating the vessel’s stability the allowance for this is made in the following manner:
In filled compartments untrimmed no compensation is necessary and the KG must be always read from the tables, which is given for the full compartment. For the filled compartment if trimmed, as given in B 1.1.3 of grain code CG of grain in case of a filled compartment trimmed shall be taken at volumetric centroid of compartment. Where Administration authorizes a (further) accounting for the adverse effect of vertical shift is done by multiplying VHM by 1.06.
Thus, in case of a filled compartment trimmed, it is always advisable that:
1. volumetric centroid is taken in calculation of KG; and
2. a factor of 1.06 is multiplied to the VHM of compartment.
In partly filled compartments the transverse volumetric heeling moments are increased by multiplying the same with factor 1.12, if the KG of the cargo is picked up from the curve for actual ullage / sounding.

Q. What are the tables of allowable heeling moments in the grain stability book?
Table of allowable heeling moments is a ready reckoner table where Master can at one glance know whether the grain stability criteria would be satisfied for the proposed cargo distribution. The grain stability booklet contains tables of maximum allowable heeling moments, compiled for a wide range of combinations of displacement and KGv. These tables are usually generated by computer using input data from the vessels cross curves of stability. A sample of such table has been shown below:

Q. What is λ0, as referred to the GZ curve drawn in respect of grain?
λ0 is like GG1 or the transverse shift of CG of the ship due to grain shift. Numerically, it is equal to

Q. Suppose the loaded displacement of a grain ship is 22110t; total volumetric heeling moment is 5596m4; and the stowage factor of grain is 1.28, how much will be λ0?

Q. Why is λ40 needed? And for this, why do we multiply by 0.8?
The upsetting anchor is actually a cosine curve with the maximum value at 0o heel, gradually reducing to 0 at 90o. Instead of making a curvilinear diagram, in order to draw the curve between 0 and 40o heel, a straight line is drawn approximating to a curve. The value of Cos 40o is 0.766, an approximate round figure of 0.8 is multiplied with λ0 to get λ40 which is the ordinate of listing arm curve at 40o.

Q. How is the average void depth found as suggested in part B of grain code?
In filled compartments which have been duly trimmed, a void exists under all boundary surfaces having an inclination to the horizontal less than 30o and that the void is parallel to the boundary surface having an average depth calculated according to the formula:
Vd = Vd1 + 0.75 (d – 600) mm
Vd = average void depth in millimeters.
Vd1 = standard void depth from table provided.
d = actual girder in millimeters.

Q. What other assumptions are made in respect of calculation of voids?
1. Within filled hatchways and in addition to any open void within the hatch cover there is a void of average depth of 150mm measured down to the grain surface from the lowest part of the hatch cover or the top of the hatch side coaming, whichever is the lower.

2. In a ‘filled compartment, untrimmed’ which is exempted from trimming outside the periphery of the hatchway shall be assumed that the surface of the grain after loading will slope into the void space underdeck, in all directions, at an angle of 30o to the horizontal from the edge of the opening which establishes the void.

3. The resulting grain surface after shifting shall be assumed to be at 15o to the horizontal. In calculating the maximum void area that can be formed against a longitudinal structural member, the effects of any horizontal surfaces, e.g. flanges or face bars, shall be ignored. The total areas of the initial and final voids shall be equal.
4. The volume of final void is equal to the volume of earlier void. In trying to maintain it if the longitudinal girder or coaming is not deep enough the void will shift further. This is explained with the following illustration:

AB: Any area in excess of that which can be formed against the girder at B shall transfer to the final void area in the hatchway. “
AB: Any area in excess of that which can be formed against the girder at E shall transfer to the final void area on the high side.

Q. What is the assumption in respect of volumetric heeling moment of a partly filled compartment?
The assumptions are as follows:

1. When the free surface of the bulk grain has not been secured in accordance with the regulations provided in part A, it shall be assumed that the grain surface after shifting shall be at 25o to the horizontal.
2. In a partly filled compartment, a division is fitted, shall extend from one eight of the maximum breadth of the compartment above the level of the grain surface and to the same distance below the grain surface.

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